A Physical Interpretation of Vibration Frequency and Amplitude Ratios for Waviness Prediction in Turning

Machine-tool vibrations adversely influence surface topography generation mechanisms, often resulting in periodic waviness marks showing a helix pattern. The interaction of tool geometry, process kinematics, and machine-tool vibrations is governed by the frequency and amplitude ratios of the tool-workpiece vibration motion. Indeed, a single-frequency vibration generates multiple helix patterns—mainly the tool feed, aliased and sub-Nyquist helix—on the surface topography. The spatial features of each helix pattern, defined by the wavelength, number of threads, and orientation, have different analytic relations with the frequency ratio. This work studies the influence of cutting parameters—spindle speed, feed per revolution, and tool nose radius—on the frequency and amplitude ratios governing the formation of waviness marks in turning. The analysis considers a range of turning processes, acknowledging that the transition from coarse to diamond turning alters the range of amplitude ratios, thereby modifying the dominant waviness pattern. By evaluating physical quantities, the study clarifies how machining conditions shape the resulting waviness patterns across different turning processes. Besides, the results demonstrate that surface waviness is highly sensitive to not only the tool-workpiece vibration motion but also cutting parameters and provides essential information for identifying the underlying vibration frequency. Understanding and controlling the influence of cutting parameters is therefore critical—both to minimize the impact of vibrations on the generated waviness and to enable accurate fault diagnosis.